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We report simultaneous detection of twin kHz and $\sim 40$ Hz quasi-periodic oscillations (QPOs) in the time-resolved analysis of the AstroSat/LAXPC observation of the neutron star low mass X-ray binary, 4U 1728-34. We present the first robust detection of multiple sets of QPO triplets from a single observation whose frequencies are mutually correlated and consistent with their identification as the orbital, periastron and twice the nodal precessions frequencies. The observed relations, along with the known spin of the neutron star, put constraints on the mass and the ratio of moment of inertia to the mass of the neutron star to be $M^*_\odot = 1.92\pm 0.01$ and $I_{45}/M^*_\odot = 1.07\pm 0.01$ under the simplistic assumption that the metric is a Kerr one. We further investigate the correlation between the kHz QPOs and the spectral parameters of the source using all AstroSat observations from 2016--2019. We found that all eight epochs fall into two accretion regimes, namely AR1 and AR2, with accretion rates of $\sim$ $3 \times 10^{16} \, \text{g} \, \text{s}^{-1}$ and $7 \times 10^{16} \, \text{g} \, \text{s}^{-1}$, respectively. Notably, we find that for AR1, the lower kHz QPO frequecncy ($\nu_{\text{L}}$) is always $<$500 Hz, whereas for AR2 it is $\gtrsim$500 Hz. While the spectral index shows no significant correlation with $\nu_{\text{L}}$, the coronal parameters exhibit systematic evolution. For AR1, the coronal electron temperature (kT$_e$) and optical depth ($\tau$) are $\sim$10 and $\sim$5 keV, respectively. In contrast, for AR2, kT$_e$ decreases to $\sim$3 keV and $\tau$ increases to $\sim$12, showing correlations with $\nu_{\text{L}}$, with Spearman's rank correlation coefficients of $-0.78$, $0.71$, respectively. The transition of spectral parameters at $\nu_{\text{L}} \sim500$ Hz suggests the presence of a critical QPO frequency governed by the accretion state of the source, highlighting a strong coupling between millisecond timing phenomena and the accretion dynamics in 4U 1728–34.